few_shots: Example:
Problem/activity:
Task
Cruz and Erica were both getting ready for soccer.
Cruz ran 1 lap around the school.
Erica ran 3 laps around the playground.
Erica said,
I ran more laps, so I ran farther.
Cruz said,
4 laps around the school is 1 mile, but it takes 12 laps around the playground to go 1 mile. My laps are much longer, so I ran farther.
Who is right? Draw a picture to help you explain your answer.


Mathematical concept/skill options: 
A. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
B. Extend understanding of fraction equivalence and ordering.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
C. Use equivalent fractions as a strategy to add and subtract fractions.
D. Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
E. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
F. Understand decimal notation for fractions, and compare decimal fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.


Thought: In this problem, students learn to recognize equivalent fractions. That is, three laps around the playground is 3/12 mile, which is equivalent to 1/4, which is one lap around the school.
Answer: B

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_000212

4
options: Rewrite rational expressions.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Generate and analyze patterns.

Represent and analyze quantitative relationships between dependent and independent variables.

Represent and solve problems involving addition and subtraction.

Create equations that describe numbers or relationships

Interpret the structure of expressions.

Gain familiarity with factors and multiples.

Understand properties of multiplication and the relationship between multiplication and division.

Represent and solve equations and inequalities graphically.

Add and subtract within 20.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Write and interpret numerical expressions.

Understand solving equations as a process of reasoning and explain the reasoning.

Work with radicals and integer exponents.

Work with equal groups of objects to gain foundations for multiplication.

Perform arithmetic operations on polynomials.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Understand and apply properties of operations and the relationship between addition and subtraction.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Solve systems of equations.

Solve equations and inequalities in one variable.

Write expressions in equivalent forms to solve problems.

Reason about and solve one-variable equations and inequalities.

Analyze patterns and relationships.

Understand the connections between proportional relationships, lines, and linear equations.

Use the four operations with whole numbers to solve problems.

Use properties of operations to generate equivalent expressions.

Use polynomial identities to solve problems.

Multiply and divide within 100.

Represent and solve problems involving multiplication and division.

Work with addition and subtraction equations.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Understand the relationship between zeros and factors of polynomials.
problem_activity: Activity
The activity is an opportunity to practice evaluating quadratic expressions for a negative value of the variable, and choosing parameters of an equation that will result in its graph looking a certain way.
Launch
Arrange students in groups of 2. Give students two minutes of quiet work time on the first question, and ask them to check their answers with their partner before starting the second question. Call attention to the scale on the axes. Identify students who use the scale to select the parameters for their linear equation.
Student Facing
Evaluate each expression when
\(x\)
is -3.
\(x^2\)
\(\text-x^2\)
\(x^2+20\)
\(\text-x^2+20\)
For each graph, come up with an equation that the graph could represent. Verify your equation using graphing technology.
[IMG]
Student Response
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Activity Synthesis
Invite students to share various equations that each graph could represent. Use different but equally correct equations to help students generalize. For example, either
\(y=x+15\)
or
\(y=x+12\)
makes sense for graph C, because it looks like
\(y=x\)
, and is shifted up by some number between 10 and 20. So we know that the equation this graph represents is in the form
\(y=x+b\)
, where
\(b\)
is positive, even though we can’t tell its exact value from the given information.


correct_option_index: 19